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<jats:title>Abstract</jats:title> <jats:p>Detecting continuous nanohertz gravitational waves (GWs) generated by individual close binaries of supermassive black holes (CB-SMBHs) is one of the primary objectives of pulsar timing arrays (PTAs). The detection sensitivity is slated to increase significantly as the number of well-timed millisecond pulsars will increase by more than an order of magnitude with the advent of next-generation radio telescopes. Currently, the Bayesian analysis pipeline using parallel tempering Markov Chain Monte Carlo has been applied in multiple studies for CB-SMBH searches, but it may be challenged by the high dimensionality of the parameter space for future large-scale PTAs. One solution is to reduce the dimensionality by maximizing or marginalizing over uninformative parameters semianalytically, but it is not clear whether this approach can be extended to more complex signal models without making overly simplified assumptions. Recently, the method of diffusive nested (DNest) sampling has shown capability in coping with high dimensionality and multimodality effectively in Bayesian analysis. In this paper, we apply DNest to search for continuous GWs in simulated pulsar timing residuals and find that it performs well in terms of accuracy, robustness, and efficiency for a PTA including <jats:inline-formula> <jats:tex-math> <?CDATA ${ \mathcal O }({10}^{2})$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac25fcieqn1.gif" xlink:type="simple" /> </jats:inline-formula> pulsars. DNest also allows a simultaneous search of multiple sources elegantly, which demonstrates its scalability and general applicability. Our results show that it is convenient and also highly beneficial to include DNest in current toolboxes of PTA analysis.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>PSR J1813–1749 has peculiarities that make it a very interesting object of study. It is one of the most energetic and the most scattered pulsars known. It is associated with HESS J1813–178, one of the brightest and most compact TeV sources in the sky. Recently, Ho et al. used archival X-ray Chandra observations separated by more than 10 yr and determined that the total proper motion of PSR J1813–1749 is ∼66 mas yr<jats:sup>−1</jats:sup>, corresponding to a velocity of ∼1900 km s<jats:sup>−1</jats:sup> for a distance of 6.2 kpc. These results would imply that this pulsar is the fastest neutron star known in the Galaxy and, by estimating the angular separation with respect to the center of the associated supernova remnant, has an age of only ∼300 yr, making it one of the youngest pulsars known. Using archival high angular resolution VLA observations taken over 12 yr we have estimated the radio proper motions of PSR J1813–1748 to be much smaller: (<jats:inline-formula> <jats:tex-math> <?CDATA ${\mu }_{\alpha }\cdot \cos (\delta ),{\mu }_{\delta }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:msub> <mml:mo>·</mml:mo> <mml:mi>cos</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>δ</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>δ</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac312fieqn1.gif" xlink:type="simple" /> </jats:inline-formula>) = (−5.0 ± 3.7, −13.2 ± 6.7) mas yr<jats:sup>−1</jats:sup>, or a total proper motion of 14.8 ± 5.9 mas yr<jats:sup>−1</jats:sup>. The positions referenced against quasars make our results reliable. We conclude that PSR J1813–1749 is not a very fast moving source. Its kinematic age using the new total proper motion is ∼1350 yr. This age is consistent within a factor of a few with the characteristic age of the pulsar and with the age estimated from the broadband spectral energy distribution of HESS J1813–178, as well as the age of the associated supernova remnant.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Asteroseismology of bright stars has become increasingly important as a method to determine the fundamental properties (in particular ages) of stars. The Kepler Space Telescope initiated a revolution by detecting oscillations in more than 500 main-sequence and subgiant stars. However, most Kepler stars are faint and therefore have limited constraints from independent methods such as long-baseline interferometry. Here we present the discovery of solar-like oscillations in <jats:italic>α</jats:italic> Men A, a naked-eye (<jats:italic>V</jats:italic> = 5.1) G7 dwarf in TESS’s southern continuous viewing zone. Using a combination of astrometry, spectroscopy, and asteroseismology, we precisely characterize the solar analog <jats:italic>α</jats:italic> Men A (<jats:italic>T</jats:italic> <jats:sub>eff</jats:sub> = 5569 ± 62 K, <jats:italic>R</jats:italic> <jats:sub>⋆</jats:sub> = 0.960 ± 0.016 <jats:italic>R</jats:italic> <jats:sub>⊙</jats:sub>, <jats:italic>M</jats:italic> <jats:sub>⋆</jats:sub> = 0.964 ± 0.045 <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub>). To characterize the fully convective M dwarf companion, we derive empirical relations to estimate mass, radius, and temperature given the absolute Gaia magnitude and metallicity, yielding <jats:italic>M</jats:italic> <jats:sub>⋆</jats:sub> = 0.169 ± 0.006 <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub>, <jats:italic>R</jats:italic> <jats:sub>⋆</jats:sub> = 0.19 ± 0.01 <jats:italic>R</jats:italic> <jats:sub>⊙</jats:sub>, and <jats:italic>T</jats:italic> <jats:sub>eff</jats:sub> = 3054 ± 44 K. Our asteroseismic age of 6.2 ± 1.4 (stat) ± 0.6 (sys) Gyr for the primary places <jats:italic>α</jats:italic> Men B within a small population of M dwarfs with precisely measured ages. We combined multiple ground-based spectroscopy surveys to reveal an activity cycle of <jats:italic>P</jats:italic> = 13.1 ± 1.1 yr for <jats:italic>α</jats:italic> Men A, a period similar to that observed in the Sun. We used different gyrochronology models with the asteroseismic age to estimate a rotation period of ∼30 days for the primary. Alpha Men A is now the closest (<jats:italic>d</jats:italic> = 10 pc) solar analog with a precise asteroseismic age from space-based photometry, making it a prime target for next-generation direct-imaging missions searching for true Earth analogs.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The Ly<jats:italic>α</jats:italic> luminosity function (LF) of Ly<jats:italic>α</jats:italic> emitters (LAEs) has been used to constrain the neutral hydrogen fraction in the intergalactic medium (IGM) and thus the timeline of cosmic reionization. Here we present the results of a new narrowband imaging survey for <jats:italic>z</jats:italic> = 7.3 LAEs in a large area of ∼3 deg<jats:sup>2</jats:sup> with Subaru/Hyper Suprime-Cam. No LAEs are detected down to <jats:italic>L</jats:italic> <jats:sub>Ly<jats:italic>α</jats:italic> </jats:sub> ≃ 10<jats:sup>43.2</jats:sup> erg s<jats:sup>−1</jats:sup> in an effective cosmic volume of ∼2 × 10<jats:sup>6</jats:sup> Mpc<jats:sup>3</jats:sup>, placing an upper limit on the bright part of the <jats:italic>z</jats:italic> = 7.3 Ly<jats:italic>α</jats:italic> LF for the first time and confirming a decrease in bright LAEs from <jats:italic>z</jats:italic> = 7.0. By comparing this upper limit with the Ly<jats:italic>α</jats:italic> LF in the case of fully ionized IGM, which is predicted using an observed <jats:italic>z</jats:italic> = 5.7 Ly<jats:italic>α</jats:italic> LF on the assumption that the intrinsic Ly<jats:italic>α</jats:italic> LF evolves in the same way as the UV LF, we obtain the relative IGM transmission <jats:inline-formula> <jats:tex-math> <?CDATA ${T}_{\mathrm{Ly}\alpha }^{\mathrm{IGM}}(7.3)/{T}_{\mathrm{Ly}\alpha }^{\mathrm{IGM}}(5.7)\lt 0.77$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>Ly</mml:mi> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>IGM</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mn>7.3</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>Ly</mml:mi> <mml:mi>α</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>IGM</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mn>5.7</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mn>0.77</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac308bieqn1.gif" xlink:type="simple" /> </jats:inline-formula> and then the volume-averaged neutral fraction <jats:italic>x</jats:italic> <jats:sub>H I</jats:sub>(7.3) &gt; 0.28. Cosmic reionization is thus still ongoing at <jats:italic>z</jats:italic> = 7.3, consistent with results from other <jats:italic>x</jats:italic> <jats:sub>H I</jats:sub> estimation methods. A similar analysis using literature Ly<jats:italic>α</jats:italic> LFs finds that at <jats:italic>z</jats:italic> = 6.6 and 7.0, the observed Ly<jats:italic>α</jats:italic> LF agrees with the predicted one, consistent with full ionization.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We present 150 MHz, 1.4 GHz, and 3 GHz radio imaging (LoTSS, FIRST, and VLASS) and spatially resolved ionized gas characteristics (SDSS IV-MaNGA) for 140 local (<jats:italic>z</jats:italic> &lt; 0.1) early-type red geyser galaxies. These galaxies have a low star formation activity (with a star formation rate, SFR, ∼ 0.01 <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub> yr<jats:sup>−1</jats:sup>), but show unique extended patterns in spatially resolved emission-line maps that have been interpreted as large-scale ionized winds driven by active galactic nuclei (AGN). In this work, we confirm that red geysers host low-luminosity radio sources (<jats:italic>L</jats:italic> <jats:sub>1.4GHz</jats:sub> ∼ 10<jats:sup>22</jats:sup> <jats:italic>WHz</jats:italic> <jats:sup>−1</jats:sup>). Out of 42 radio-detected red geysers, 32 are spatially resolved in LoTSS and FIRST, with radio sizes varying between ∼5–25 kpc. Three sources have radio sizes exceeding 40 kpc. A majority display a compact radio morphology and are consistent with either low-power compact radio sources (FR0 galaxies) or radio-quiet quasars. They may be powered by small-scale AGN-driven jets that remain unresolved at the current 5″ resolution of radio data. The extended radio sources, not belonging to the “compact” morphological class, exhibit steeper spectra with a median spectral index of −0.67, indicating the dominance of lobed components. The red geysers hosting extended radio sources also have the lowest specific SFRs, suggesting they either have a greater impact on the surrounding interstellar medium or are found in more massive halos on average. The degree of alignment of the ionized wind cone and the extended radio features are either 0° or 90°, indicating possible interaction between the interstellar medium and the central radio AGN.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We collect 133 fast radio bursts (FRBs), including 110 nonrepeating and 23 repeating ones, and systematically investigate their observational properties. To check the frequency dependence of FRB classifications, we define our samples with a central frequency below/above 1 GHz as subsample I/II. First, we find that there is a clear bimodal distribution of pulse width for subsample I. If we classify FRBs into short FRBs (<jats:italic>s</jats:italic>FRBs; &lt;100 ms) and long FRBs (<jats:italic>l</jats:italic>FRBs; &gt;100 ms) as done for short and long gamma-ray bursts (GRBs), the <jats:italic>s</jats:italic>FRBs at higher central frequency are commonly shorter than those at lower central frequency not only for nonrepeating but also repeating <jats:italic>s</jats:italic>FRBs. Second, we find that fluence and peak flux density are correlated with a power-law relation of <jats:inline-formula> <jats:tex-math> <?CDATA $F\propto {S}_{p,\mathrm{obs}}^{\gamma }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>F</mml:mi> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>obs</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac3085ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> for both <jats:italic>s</jats:italic>FRBs and <jats:italic>l</jats:italic>FRBs whose distributions are obviously different. Third, the <jats:italic>l</jats:italic>FRBs with isotropic energies ranging from 10<jats:sup>42</jats:sup> to 10<jats:sup>44</jats:sup> erg are more energetic than the <jats:italic>s</jats:italic>FRBs in the <jats:italic>F</jats:italic>–<jats:italic>DM</jats:italic> <jats:sub>EX</jats:sub> plane, indicating that they are two representative types. Finally, it is interesting to note that the peak flux density behaves independently on the redshift when the distance of the FRBs becomes far enough, which is similar to the scenario of the peak flux evolving with redshift in the field of GRBs. We predict that fainter FRBs at a higher redshift of <jats:italic>z</jats:italic> &gt; 2 can be successfully detected by FAST and the Square Kilometre Array in the near future.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>With the aid of the ion densities measured by the Neutral Gas and Ion Mass Spectrometer and the solar wind dynamic pressures measured by the Solar Wind Ion Analyzer on board the Mars Atmosphere and Volatile EvolutioN, we investigate the modulation of a sequence of ion species in the Martian topside ionosphere by the upstream solar wind condition. Almost all ion species, except for <jats:inline-formula> <jats:tex-math> <?CDATA ${\mathrm{CO}}_{2}^{+}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>CO</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac2bfcieqn1.gif" xlink:type="simple" /> </jats:inline-formula> and OCOH<jats:sup>+</jats:sup>, are very sensitive to the variation of the solar wind condition, and their densities decrease with increasing solar wind dynamic pressure. The response of the topside ion distribution to the variation of the solar wind condition is also found to be remarkably related to the magnetic field orientation, in that the solar wind modulation occurs mainly over regions with near-horizontal field lines. These observations imply substantially enhanced outflow velocities for all ion species under high solar wind dynamic pressures when the ambient magnetic fields are near-horizontal.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We use 3 mm continuum NOrthern Extended Millimeter Array and NH<jats:sub>3</jats:sub> Very Large Array observations toward the First Hydrostatic Core (FHSC) candidate CB 17 MMS in order to reveal the dust structure and gas properties to 600–1100 au scales and to constrain its evolutionary stage. We do not detect any compact source at the previously identified 1.3 mm point source, despite expecting a minimum signal-to-noise ratio of 9. The gas traced by NH<jats:sub>3</jats:sub> exhibits subsonic motions, with an average temperature of 10.4 K. A fit of the radial column density profile derived from the ammonia emission finds a flat inner region of radius ∼1800 au and a central density of ∼6 × 10<jats:sup>5</jats:sup> cm<jats:sup>−3</jats:sup>. Virial and density structure analysis reveals the core is marginally bound (<jats:italic>α</jats:italic> <jats:sub>vir</jats:sub> = 0.73). The region is entirely consistent with that of a young starless core, hence ruling out CB 17 MMS as an FHSC candidate. Additionally, the core exhibits a velocity gradient aligned with the major axis, showing an arc-like structure in the position–velocity diagram and an off-center region with high velocity dispersion, caused by two distinct velocity peaks. These features could be due to interactions with the nearby outflow, which appears to deflect due to the dense gas near the NH<jats:sub>3</jats:sub> column density peak. We investigate the specific angular momentum profile of the starless core, finding that it aligns closely with previous studies of similar radial profiles in Class 0 sources. This similarity to more evolved objects suggests that motions at 1000 au scales are determined by large-scale dense cloud motions, and may be preserved throughout the early stages of star formation.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Improving the performance of solar flare forecasting is a hot topic in the solar physics research field. Deep learning has been considered a promising approach to perform solar flare forecasting in recent years. We first used the generative adversarial networks (GAN) technique augmenting sample data to balance samples with different flare classes. We then proposed a hybrid convolutional neural network (CNN) model (<jats:italic>M</jats:italic>) for forecasting flare eruption in a solar cycle. Based on this model, we further investigated the effects of the rising and declining phases for flare forecasting. Two CNN models, i.e., <jats:italic>M</jats:italic> <jats:sub>rp</jats:sub> and <jats:italic>M</jats:italic> <jats:sub>dp</jats:sub>, were presented to forecast solar flare eruptions in the rising phase and declining phase of solar cycle 24, respectively. A series of testing results proved the following. (1) Sample balance is critical for the stability of the CNN model. The augmented data generated by GAN effectively improved the stability of the forecast model. (2) For C-class, M-class, and X-class flare forecasting using Solar Dynamics Observatory line-of-sight magnetograms, the means of the true skill statistics (TSS) scores of <jats:italic>M</jats:italic> are 0.646, 0.653, and 0.762, which improved by 20.1%, 22.3%, and 38.0% compared with previous studies. (3) It is valuable to separately model the flare forecasts in the rising and declining phases of a solar cycle. Compared with model <jats:italic>M</jats:italic>, the means of the TSS scores for No-flare, C-class, M-class, and X-class flare forecasting of the <jats:italic>M</jats:italic> <jats:sub>rp</jats:sub> improved by 5.9%, 9.4%, 17.9%, and 13.1%, and those of the <jats:italic>M</jats:italic> <jats:sub>dp</jats:sub> improved by 1.5%, 2.6%, 11.5%, and 12.2%.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>This work establishes the most complete sample of red supergiants (RSGs) in 12 low-mass galaxies (WLM, IC 10, NGC 147, NGC 185, IC 1613, Leo A, Sextans B, Sextans A, NGC 6822, Pegasus Dwarf, SMC, and LMC) of the Local Group, which forms a solid basis to study the properties of RSGs as well as the star formation rate and initial mass function of the galaxies. After removing the foreground dwarf stars by their obvious branch in the near-infrared color–color diagram (<jats:inline-formula> <jats:tex-math> <?CDATA ${\left(J-H\right)}_{0}/{\left(H-K\right)}_{0}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>−</mml:mo> <mml:mi>H</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>−</mml:mo> <mml:mi>K</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac307bieqn1.gif" xlink:type="simple" /> </jats:inline-formula>) with the UKIRT/WFCAM and 2MASS photometry as well as the Gaia/EDR3 measurements of proper motion and parallax, RSGs are identified from their location in the color–magnitude diagram <jats:inline-formula> <jats:tex-math> <?CDATA ${\left(J-K\right)}_{0}/{K}_{0}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>−</mml:mo> <mml:mi>K</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac307bieqn2.gif" xlink:type="simple" /> </jats:inline-formula> of the member stars of the specific galaxy. A total of 2190 RSGs are found in 10 dwarf galaxies, and additionally, 4823 and 2138 RSGs are found in LMC and SMC, respectively. The locations of the tip of the red giant branch in the <jats:inline-formula> <jats:tex-math> <?CDATA ${\left(J-K\right)}_{0}/{K}_{0}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>−</mml:mo> <mml:mi>K</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac307bieqn3.gif" xlink:type="simple" /> </jats:inline-formula> diagram are determined to serve as an indicator of the metallicity and distance modulus of the galaxies.</jats:p>